Uncertain Optimal Control by Yuanguo Zhu

Author:Yuanguo Zhu
Language: eng
Format: epub, pdf
ISBN: 9789811321344
Publisher: Springer Singapore

5.2 Bang–Bang Control for Multistage Uncertain Systems

Consider the following uncertain optimal control problem with a linear objective function subject to an uncertain linear system:

(5.12)

where and are constants for all j. In addition, , , , are independent uncertain variables with expected values , respectively.

Theorem 5.3

([2]) The optimal controls of (5.12) are provided by

and the optimal values are

where

for .

Proof

Denote the optimal control for the above problem by , , , . By using the recurrence Eq. (4.​2), we have

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